Suman Majumder

Universality in fluid domain coarsening: The case of vapor-liquid transition

Domain growth during the kinetics of phase separation is studied following vapor-liquid transition in a single component Lennard-Jones fluid. Results are analyzed after appropriately mapping the continuum snapshots obtained from extensive molecular-dynamics simulations to a simple cubic lattice. For near-critical quench interconnected domain morphology is observed. A brief period of slow diffusive growth is followed by a linear viscous hydrodynamic growth that lasts for an extended period of time. This result is in contradiction with earlier reports of late-time growth exponent 1/2 that questions the uniqueness of the non-equilibrium universality for liquid-liquid and vapor-liquid transitions.

Finite-size effects in dynamics: Critical vs. coarsening phenomena

Finite-size effects in systems with diverging characteristic length scale have been addressed via state-of-the-art Monte Carlo and molecular-dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid transitions. Our simulations, combined with the appropriate application of the finite-size scaling theory, confirm various non-trivial singularities in equilibrium dynamic critical phenomena and non-equilibrium domain coarsening phenomena, as predicted by analytical theories. We convincingly demonstrate that the finite-size effects in the domain growth problems, with conserved order parameter dynamics, is weak and universal, irrespective of the transport mechanism. This result is strikingly different from the corresponding effects in critical dynamics. In critical phenomena, the difference in finite-size effects between statics and dynamics is also discussed.

Diffusive domain coarsening: early time dynamics and finite-size effects.

We study the diffusive dynamics of phase separation in a symmetric binary (A + B) mixture with a 50:50 composition of A and B particles, following a quench below the demixing critical temperature, both in spatial dimensions d=2 and d=3. The particular focus of this work is to obtain information about the effects of system size and correction to the growth law via the appropriate application of the finite-size scaling method to the results obtained from the Kawasaki exchange Monte Carlo simulation of the Ising model. Observations of only weak size effects and a very small correction to scaling in the growth law are significant. The methods used in this work and information thus gathered will be useful in the study of the kinetics of phase separation in fluids and other problems of growing length scale. We also provide a detailed discussion of the standard methods of understanding simulation results which may lead to inappropriate conclusions.

Aging in ferromagnetic ordering: full decay and finite-size scaling of autocorrelation

Nonequilibrium dynamics in Ising and Ginzburg-Landau models were studied for a nonconserved order parameter that mimics ordering in ferromagnets. The focus was on the understanding of the decay of the two time (t, t(w); t > tw) order-parameter correlation function. For this quantity, a full form has been obtained empirically which, for t ≫ t(w), provides a power-law ∼ (ℓ/ℓ(w))(-λ), ℓ and ℓ(w) being the characteristic lengths at t and tw, respectively. This empirical form was used for a finite-size scaling analysis to obtain the exponent λ in space dimensions d = 2 and 3. Our estimates of λ and understanding of the finite-size effects, for the models considered, provide useful information on the relevance of thermal noise. The values of λ obtained are in good agreement with the predictions of a theory based on Gaussian auxiliary field ansatz.

Cluster coarsening during polymer collapse: Finite-size scaling analysis

We study the kinetics of the collapse of a single flexible polymer when it is quenched from a good solvent to a poor solvent. Results obtained from Monte Carlo simulations show that the collapse occurs through a sequence of events with the formation, growth and subsequent coalescence of clusters of monomers to a single compact globule. Particular emphasis is given in this work to the cluster growth during the collapse, analyzed via the application of finite-size scaling techniques. The growth exponent obtained in our analysis is suggestive of the universal Lifshitz-Slyozov mechanism of cluster growth. The methods used in this work could be of more general validity and applicable to other phenomena such as protein folding.

Dimensionality dependence of aging in kinetics of diffusive phase separation: Behavior of order-parameter autocorrelation.

Behavior of two-time autocorrelation during the phase separation in solid binary mixtures is studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions 2 and 3 are obtained empirically. The long-time behavior is found to be power law, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Cahn-Hilliard and Ising models provide consistent results.

Effects of density conservation and hydrodynamics on aging in nonequilibrium processes.

Aging in kinetics of three different phase transitions, viz., magnetic, a binary solid, and a single component fluid, are studied via Monte Carlo and molecular dynamics simulations in three space dimensions with the objective of identifying the effects of order-parameter conservation and hydrodynamics. We observe that the relevant autocorrelations exhibit power-law decay in a ferromagnet and binary solid but with different exponents. At early time the fluid autocorrelation function nicely follows that of the binary solid, the order parameter being conserved for both of them, as opposed to a ferromagnet. At a late time the fluid data crosses over to an exponential decay which we identify as a hydrodynamic effect and we provide analytical justification for this behavior.

Coarsening and aging of lattice polymers: Influence of bond fluctuations

We present results for the nonequilibrium dynamics of collapse for a model flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds between the monomers. Results from our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a non-universal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a temperature independent growth, which can be described by a universal nonequilibrium finite-size scaling function with a non-universal metric factor. We also examine the related aging phenomenon, probed by a suitable two-time density-density autocorrelation function showing a simple power-law scaling with respect to the growing cluster size. Unlike the cluster-growth exponent αc, the nonequilibrium autocorrelation exponent λC governing the aging during the collapse, however, is independent of the bond type and strictly follows the bounds proposed by Majumder and Janke [Phys. Rev. E 93, 032506 (2016)] at all temperatures.

Evidence of aging and dynamic scaling in the collapse of a polymer.

We investigate a newly framed two-time property for the nonequilibrium evolution dynamics during the collapse of a homopolymer via Monte Carlo simulations of a model polymer. Our results show evidence of aging effects, as observed in the slow dynamics of structural and spin glasses, along with the presence of a dynamic scaling of the autocorrelation function ∼x(-λ(c)) (x being the ratio of the cluster sizes at two different times). We estimate the value of λ(c) unambiguously by applying a finite-size scaling analysis to the numerical data. The value thus obtained obeys a bound which we predict via general theoretical arguments. The results presented should be of general validity and may trigger direct experimental verification in single-polymer dynamics.

Aging and related scaling during the collapse of a polymer

We present results showing aging during the collapse of a polymer chain quenched from an expanded state to the globular phase via Monte Carlo dynamics of a model homopolymer. The constructed two-time correlation function, an analogue of the density- density autocorrelation, shows a power-law scaling with respect to the size of monomer clusters formed during the collapse. The numerical estimates obtained at different quench temperatures are in agreement with a theoretically predicted bound for the decay exponent governing the scaling behavior.